# Math Help - region R - need your explaination.

1. ## region R - need your explaination.

Given z=x^2+y^2

I have the following information for region R.
R = (x,y) such that x^2 +(y-1/2)^2 < or = 1/4

why R = ( r,theta) such that 0< or = r < or = sin theta ? I don't understand how r = sin theta. Could you please explain to me? Thank you very much.

2. Given z=x^2+y^2

And also z=y

3. Originally Posted by kittycat
Given z=x^2+y^2

I have the following information for region R.
R = (x,y) such that x^2 +(y-1/2)^2 < or = 1/4

why R = ( r,theta) such that 0< or = r < or = sin theta ? I don't understand how r = sin theta. Could you please explain to me? Thank you very much.
$0 \le x^2 + \left( y - \frac 12 \right)^2 = x^2 + y^2 - y + \frac 14 \le \frac 14$

$\Rightarrow 0 \le x^2 + y^2 \le y$

switch to polar coordinates

$\Rightarrow 0 \le r^2 \le r \sin \theta$

divide through by $r$

$\Rightarrow 0 \le r \le \sin \theta$